Motor displacement reduction

I have a little project, I am building a simple lift that is moved with cable by a 3-phase motor which has it's speed controlled by variable frequency drive. I am going to be implementing PID control into the VFD via PLC that will be based off of a distance reading from an ultrasonic sensor for error detection. There are separate levels with different setpoints in the program. Problem is that I will not be using much load on the lift, and it will not move very fast. The 3-phase motor which meets these specifications is not used commonly and is very expense. So I purchased a 1/3HP 3-phase motor that is rated at 1750RPM for a cheap price. Obviously the speed is too fast for my application. I figured that I would use pulleys to reduce the speed of the lift by 1/4, using a small pulley on motor and a larger pulley with a bearing. I would use a double grooved pulley which would have a belt going to the motor pulley, which was smaller, then have a cable which goes from the pulley to the lift and then finally to another pulley on top w/ a bearing. While I was looking for pulleys, it occurred to me that the only change that will occur is the rotational speed. The displacement will be the same, thus lift will move same speed regardless of pulley size. I would have to somehow attach a smaller pulley onto the speed reduction pulley. But the problem is that if i'm off by a a few mm, the pulley will move away from the cable while spinning. I can't find a double grooved pulley which does this anywhere. I was wondering if there was a little solution for a dilemma. I was thinking about using gears, but I am not sure how to go about this. The shaft on my motor is 5/8 drive, so i will probably need something that is a 5/8 keyed bore. Where could I go to purchase these parts?

If pulleys won't work neither will gears. They perform the basically the same function.
Are you sure you understand how pulleys work? I can't think of a lift design where pulleys can't do what you need..

Your proposed belt & pulley solution must drive an input shaft at the reduced speed. This will make the lift speed reduced in the same way. Looks like this should work, provided you choose the right pulley diameters.

You cannot do anything with gears that you could not do with pulleys and a belt in terms of speed change.

Ok, ill stick with my pulley idea. From what I understand is that if you go from a smaller pulley to a larger pulley, the angular speed will be reduced as it has a larger diameter. So for my case, I would have to have small pulley going to a large pulley, and then have a smaller pulley attached to that larger pulley going to the lift, and higher up pulley. This way the speed will be slower than motor pulley, yet displace less distance than the pulley reducing the rotational speed.

For example, a 2in pulley mounted to motor shaft. There would be a belt going from that to another, larger 8in pulley. Then I would have to have another 2in pulley attached to that pulley which would go to the lift and final pulley, also 2inches at top. This way I can have a slower speed, and less distance displacement of lift.

But where can I find a double grooved pulley that does that function above? It would have to have a bearing aswell.

Your use of the word "displace" is a bit fuzzy!! What do you mean when you speak of a pulley displacing?

The usual word is rotation (I think that is what you are getting at here), and when a small pulley drives a larger pulley, the small pulley has to rotate through a larger angle than that turned by the larger pulley. The arc length of belt payed off one pulley is equal to the arc length of belt wrapped onto the second pulley in all cases (neglecting belt stretch).